Question

Factorise: x³ + 3x² + 3x - 7​

Answer 1

$\huge\underline\mathfrak\red{Solution}$

→ x³ + 3x² + 3x - 7

= (x³ + 3x² + 3x + 1)-7 -1 [adding & subtracting 1]

= (x + 1)³ - 8 = (x + 1)² - 2³

= (x + 1 - 2) × {(x + 1)² + 2(x + 1) + 2²}

= (x - 1) (x² + 4x + 7)

=> (x³ + 3x² + 3x - 7) = (x - 1)(x² + 4x + 7).

$\huge\mathbb\blue{THANK\:YUH!}$

Answer 2

x³ - 3x² + 3x + 7

= x³ + x² - 4x² - 4x + 7x + 7

= x²(x + 1) + -4x (x + 1) + 7 (x + 1)

= (x + 1) (x² - 4x + 7),